Symbolic ARMA Model Analysis

ARMA models provide a parsimonious and flexible mechanism for modeling the evolution of a time series. Some useful measures of these models (e.g., the autocorrelation function or the spectral density function) are tedious to compute by hand. This paper uses a computer algebra system, not simulation, to calculate measures of interest associated with ARMA models.     

Medium range forecasting of power system load (energy) demand

The most popular Box-Jenkins method, generally used for short-term forecasting, is modified to make it suitable for medium and long-range forecasting. The non-stationarity and seasonality have been identified and, after removing trends and/or seasonality, the series are tested for stationarity by various methods. The series have been fitted for different auto-regressive moving average (ARMA) models in the multiplicative modes. The parameter values have been determined from autocorrelation function (a.c.f.) and partial auto-correlation function (p.a.c.f.) cor-relograms and the whiteness of the residue has been checked. A forecast has been made for energy demand for one year with the help of this model and the result has been compared with actual demand.     

Deriving the autocovariances of powers of Markov-switching GARCH models, with applications to statistical inference

A procedure is proposed for computing the autocovariances and the ARMA representations of the squares, and higher-order powers, of Markov-switching GARCH models. It is shown that many interesting subclasses of the general model can be discriminated in view of their autocovariance structures. Explicit derivation of the autocovariances allows for parameter estimation in the general model, via a GMM procedure. It can also be used to determine how many ARMA representations are needed to identify the Markov-switching GARCH parameters. A Monte Carlo study and an application to the Standard & Poor index are presented.     

非线性时间序列预报的隐多分辨ARMA模型

研究一类用于非线性时间序列预报的隐多分辨自回归滑动平均(ARMA)模型,该模型以ARMA模型为初始细水平模型(即隐多分辨模型的基本块)．证明了模型的建模精度由水平问的方差决定．研究了新模型的自相关函数结构,给出了参数估计的Bayes方法和Metropolis-Hasting算法．进一步提出了一种可以直接用于不同基本块的隐多分辨模型的非线性时间序列预报方法,证明了其比其他的线性预报方法和隐多分辨模型预报方法降低了预报误差．最后通过数值模拟和实例验证了模型和预报方法,并和其他模型进行比较,结果表明新提出模型和预报方法能够更好地描述数据的特征,提高预报的精度．     

线性随机微分方程与其ARMA形式的采样模型

本文基于自协方差函数讨论了ARMA(n,n-1)与线性随机微分方程(LSDE)的关系,证明了ARMA(n,n-1)是LSDE的采样模型的三种不同形式的充要条件(适用于不同情况)。这些充要条件是一组关于ARMA(n,n-1)与LSDE参数变换的方程。当n=1,2,3,4,5时,这组方程的实际解法及实例计算也被给出。     

A hybrid multi-order fuzzy time series for forecasting stock markets

This paper proposes a hybrid model based on multi-order fuzzy time series, which employs rough sets theory to mine fuzzy logical relationship from time series and an adaptive expectation model to adjust forecasting results, to improve forecasting accuracy. Two empirical stock markets (TAIEX and NASDAQ) are used as empirical databases to verify the forecasting performance of the proposed model, and two other methodologies, proposed earlier by Chen and Yu, are employed as comparison models. Besides, to compare with conventional statistic method, the partial autocorrelation function and autoregressive models are utilized to estimate the time lags periods within the databases. Based on comparison results, the proposed model can effectively improve the forecasting performance and outperforms the listing models. From the empirical study, the conventional statistic method and the proposed model both have revealed that the estimated time lags for the two empirical databases are one lagged period.     

非线性时间序列建模的混合自回归滑动平均模型

提出了一类用于非线性时间序列建模的混合自回归滑动平均模型(MARMA).该模型是由K个平稳或非平稳的ARMA分量经过混合得到的.讨论了MARMA模型的平稳性条件和自相关函数.给出了MARMA模型参数估计的期望极大化(expectation maximization)算法.运用贝叶斯信息准则(Bayes information criterion)来选择该模型.MARMA模型分布形式富于变化的特征使得它能够对具有多峰分布以及条件异方差的序列进行建模.通过两个实例验证了该模型,并和其他模型进行比较,结果表明MARMA模型能够更好地描述这些数据的特征.     

Identification of dynamic errors-in-variables models: Approaches based on two-dimensional ARMA modeling of the data

In this paper we propose a parametric and a non-parametric identification algorithm for dynamic errors-in-variables model. We show that the two-dimensional process composed of the input-output data admits a finite order ARMA representation. The non-parametric method uses the ARMA structure to compute a consistent estimate of the joint spectrum of the input and the output. A Frisch scheme is then employed to extract an estimate of the joint spectrum of the noise free input-output data, which in turn is used to estimate the transfer function of the system. The parametric method exploits the ARMA structure to give estimates of the system parameters. The performances of the algorithms are illustrated using the results obtained from a numerical simulation study.     

ARMA时间序列模型的研究与应用

ARMA模型是一种最常见的重要的时间序列模型,它被广泛应用到各种行业预测中,本文在给出ARMA三种模式和实现方法的同时,给出ARMA模型在股市应用的一个实例。     

Testing volatility autocorrelation in the constant elasticity of variance stochastic volatility model

The sample autocovariance of the suitably scaled squared returns of a given stock is shown here to be a consistent and asymptotically normal estimator of the theoretical autocovariance of the mean variance, when the data is generated by the Constant Elasticity of Variance stochastic volatility (CEV SV) process. By computing explicitly the asymptotic variance of the estimator, confidence bands are obtained for the theoretical autocovariance. For each one of the stock indexes S&P500, CAC40, FTSE, DAX and SMI the estimated confidence bands are compared with the theoretical autocovariances computed for several values of the model parameters. The results suggest that the CEV SV model is able to capture the empirical autocovariance detected on the observed data. Analogous results are derived for the theoretical autocorrelation function.     

Autoregressive forecast of monthly total ozone concentration: A neurocomputing approach

The present study endeavors to generate autoregressive neural network (AR-NN) models to forecast the monthly total ozone concentration over Kolkata (22°34′, 88°22′), India. The issues associated with the applicability of neural network to geophysical processes are discussed. The autocorrelation structure of the monthly total ozone time series is investigated, and stationarity of the time series is established through the periodogram. From various autoregressive moving average (ARMA) and autoregressive models fit to the time series, the autoregressive model of order 10 is identified as the best. Subsequently, 10 autoregressive neural network (AR-NN) models are generated; the 10th order autoregressive neural network model with extensive input variable selection performs the best among all the competitive models in forecasting the monthly total ozone concentration over the study zone.     

Algorithm to estimate the frequency values of rose diagrams for boundaries of map features

The FORTRAN IV program RODIA described in this paper serves to compute the frequency values of a rose diagram from the binary image of a map pattern. The two-dimensional autocovariance function of the binary image is converted into a table of intercept values by using a linear or an exponential model. The frequency values of the rose diagram are compouted from these intercept values. RODIA can be used to determine the preferred orientations of contacts between rock units and sets of contours on a map.     

An integrated framework of genetic network programming and multi-layer perceptron neural network for prediction of daily stock return: An application in Tehran stock exchange market

Evolutionary algorithms are generally used to find or generate the best individuals in a population. Whenever these algorithms are applied to agent systems, they will lead to optimal solutions. Genetic Network Programming (GNP), which contains graph networks, is one of the developed evolutionary algorithms. When the aim is to forecast the share price or return, ascending and descending trends, volatilities, recent returns, fundamental and technical factors have remarkable impacts on the prediction. This is why technical indicators are used to constitute a set of trading rules. In this paper, we apply an integrated framework consisting of GNP model along with a reinforcement learning and Multi-Layer Perceptron (MLP) neural network to classify data and also time series models to forecast the stock return. Moreover, we utilize rules of accumulation based on the GNP model’s results to forecast the return. The aim of using these models alongside one another is to estimate one-day return. The results derived from 9 stocks with regard to the Tehran Stock Exchange Market. GNP extracts a prodigious number of rules on the basis of 5 technical indicators with 3 times period. Next, MLP network classifies data and finds the similarity between future data and past data concerning a stock (5 sub-period) through classification. Subsequently, a number of conditions are established, in order to choose the best estimation between GNP-RL and ARMA. Distinct comparison with the ARMA–GARCH model, which is operated for return estimation and risk measurement in many researches, demonstrates an extended forecasting power of the proposed model, by the name of GNP–ARMA, reducing error by a mean of 16%.     

基于FARIMA模型的Internet网络业务预报

最近的网络研究发现Internet网络业务同时呈现长相关和短相关特性,因此建立可以同时描述,预报长相关和短相关特性的网络业务模型很有必要。文中给出了利用FARIMA模型进行建模和预报的方法,实验表明这种方法用于实际Internet网络trace是非常有效的,另外提供了简化FARIMA模型拟合的方法和具体步骤,这样大大缩短了模型辨识的时间,对于实际网络预报有很好的实用性。     

A hybrid model based on rough sets theory and genetic algorithms for stock price forecasting

In the stock market, technical analysis is a useful method for predicting stock prices. Although, professional stock analysts and fund managers usually make subjective judgments, based on objective technical indicators, it is difficult for non-professionals to apply this forecasting technique because there are too many complex technical indicators to be considered. Moreover, two drawbacks have been found in many of the past forecasting models: (1) statistical assumptions about variables are required for time series models, such as the autoregressive moving average model (ARMA) and the autoregressive conditional heteroscedasticity (ARCH), to produce forecasting models of mathematical equations, and these are not easily understood by stock investors; and (2) the rules mined from some artificial intelligence (AI) algorithms, such as neural networks (NN), are not easily realized.In order to overcome these drawbacks, this paper proposes a hybrid forecasting model, using multi-technical indicators to predict stock price trends. Further, it includes four proposed procedures in the hybrid model to provide efficient rules for forecasting, which are evolved from the extracted rules with high support value, by using the toolset based on rough sets theory (RST): (1) select the essential technical indicators, which are highly related to the future stock price, from the popular indicators based on a correlation matrix; (2) use the cumulative probability distribution approach (CDPA) and minimize the entropy principle approach (MEPA) to partition technical indicator value and daily price fluctuation into linguistic values, based on the characteristics of the data distribution; (3) employ a RST algorithm to extract linguistic rules from the linguistic technical indicator dataset; and (4) utilize genetic algorithms (GAs) to refine the extracted rules to get better forecasting accuracy and stock return. The effectiveness of the proposed model is verified with two types of performance evaluations, accuracy and stock return, and by using a six-year period of the TAIEX (Taiwan Stock Exchange Capitalization Weighted Stock Index) as the experiment dataset. The experimental results show that the proposed model is superior to the two listed forecasting models (RST and GAs) in terms of accuracy, and the stock return evaluations have revealed that the profits produced by the proposed model are higher than the three listed models (Buy-and-Hold, RST and GAs).     

Short-term sales forecasting with change-point evaluation and pattern matching algorithms

The hotel and car manufacturing industries share many common points in their sales forecasting. For example, both are greatly affected by the fluctuation of economy, and closely related to the inertia. According to the principle characters of forecasting problem concerning these two kinds of industries, a short-term quantitative sales forecasting model is proposed based on the economic fluctuation analysis and the na?¨ve forecasting technology. The sales time series and its curve are used to construct this model. The relative concepts of the model are presented and corresponding algorithms are brought forward. Firstly, economic fluctuation of products sales is analyzed and the historical patterns of economic fluctuation change are divided. According to the geometric characteristics of a sales curve, the best historical matching for the current status is then found out, which corresponds to the process of activating the historical experiences of a manager. Finally the changing trend of the sales curve in the next period is determined, from which the short-term sales forecasting results can be obtained. The number of scattered guests of a hotel and the short-term sales for cars manufactured by a factory are forecasted by means of the model, which shows satisfactory forecasting accuracy. In fact, the forecasting approach proposed herein is the mathematical representation of the naïve forecasting method that is a kind of regular deduction based on the similarity between historical pattern and current status. Thus, this approach is good at forecasting the time series with the similarity between historical pattern and current status no matter whether the time series is seasonal or not, and gives better forecasting accuracy than ARMA and ANN models.     

Parameter identification for a two-dimensional image fieId†

This paper presents a new approach to image enhancement based on a maximum likelihood identification method. It is assumed that the images are corrupted by a white gaussian noise field. A two-dimensional extension of the classical ARMA model is developed as a mathematical model for the image fields. Since the maximum likelihood identification leads to a parametric optimization problem, Davidon's algorithm is applied for numerical solutions. The advantage of the present method is that the enhanced images based on the predicted estimates are directly obtained from the noise-corruptod images, so that the autocovariance function of the original image is not required. To improve the quality of the enhanced images, a filtering algorithm is also derived. Digital simulation studies are carried out for various artificial images to show the feasibility of this approach.     

Correlation analysis of a discrete-time flexible arrival process

In this paper, a flexible discrete-time arrival process is introduced and its correlation properties are analyzed. The arrival process is the so-called batch-on/off model, an extension of the original on/off source used in the context of ATM networks. In the batch-on/off model, a group of arrivals may be generated at any given active slot. General distributions are assumed for the three input random variables characterizing the process: busy and idle periods, and batch size. The analysis focuses on two related processes: the process of counts and the sequence of interarrival times. For each process, an exact closed-form expression of its complete autocorrelation function is obtained. Explicit algorithms are provided to compute both autocorrelation functions, which are numerically evaluated for different distributions of the busy and idle periods and the batch size. The results provided in this paper reveal the analytical tractability of these models which, in addition to their flexibility, makes them very suitable for the performance evaluation of discrete-time communication systems and for general research in the area of queuing theory.     

Scalable processing and autocovariance computation of big functional data

This paper presents 2 main contributions. The first is a compact representation of huge sets of functional data or trajectories of continuous‐time stochastic processes, which allows keeping the data always compressed even during the processing in main memory. It is oriented to facilitate the efficient computation of the sample autocovariance function without a previous decompression of the data set, by using only partial local decoding. The second contribution is a new memory‐efficient algorithm to compute the sample autocovariance function. The combination of the compact representation and the new memory‐efficient algorithm obtained in our experiments the following benefits. The compressed data occupy in the disk 75% of the space needed by the original data. The computation of the autocovariance function used up to 13 times less main memory, and run 65% faster than the classical method implemented, for example, in the R package.     

基于ARMA和小波变换的交通流预测模型研究

基于小波变换理论和自回归滑动平均(ARMA)时间序列模型的相关知识,研究了智能交通优化控制系统中的交通流量的预测问题。首先,在对实际监测的交通流量数据进行小波变换处理的基础上,建立交通流量的预测模型;然后,利用最小二乘法理论对ARMA模型的参数结构进行了详细地分析;同时给出基于小波变换和ARMA模型的交通流优化控制系统的运行机理并设计出相应的网络拓扑模型和数据传输模型;最后,用某交通观测站的实测数据对模型进行实际仿真。仿真结果表明,文中所设计的模型和算法是有效的。